Obama’s missteps and reversals – critics call them outright lies – on health care also vividly spotlight his most stubborn flaws. His lack of management experience and expertise, inability to build consensus and reliance on academic rather than practical fixes now come in for new scrutiny.

Moments such as these have proved to be lines of demarcation, crucial tests of presidential mettle that in some cases defined a president’s stewardship.

George W. Bush was hurt by his government’s response to Hurricane Katrina in 2005. Bill Clinton’s sexual relations with Monica Lewinsky confirmed that he was a reckless womanizer. In 1986, the Iran-Contra scandal was vivid evidence that Ronald Reagan was, as many suspected, out of touch with his own administration.

Reagan’s and Clinton’s legacies did survive nicely, thanks largely to booming economies and sheer force of personality. Bush, who never mastered mass communication and who faced rising frustration with the war in Iraq, had no such luck. His party lost control of Congress a year after Katrina and, a year after that, the economy went into its worst tailspin since the Great Depression.

Now it’s Obama’s turn to be judged with the same kinds of raw, telling challenges his predecessors confronted, all problems of their own making and, coincidentally, all in their second terms.

Republicans are eagerly teeing up the catchphrases and the metaphors. “A Category 5 political hurricane,” said Rep. Greg Walden, the Oregon Republican who heads his party’s congressional campaign committee. “I think 2014 will be a referendum on the failures of this administration and the philosophy that big government has the answers.”

Walden also showed he’s reading the public mood. Thanks to Obamacare, he said, “a bond of trust has been broken.”

Trust is certainly lagging: More people mentioned dissatisfaction with government than anything else in a Nov. 7-10 Gallup poll that asked Americans about the most important problem the nation faces. The cost and quality of health care came second.

And they don’t think their leaders are going to help much. Obama’s approval numbers have been hovering around 40 percent, the lowest of his presidency. Congress’ approval rating is down to 9 percent, the worst since Gallup started asking the question 39 years ago.

The White House says it’ll try to turn those numbers around by focusing on making the Affordable Care Act work.

“This is, obviously, a challenge, and we’re facing the challenge, and we’re up to the challenge,” Press Secretary Jay Carney said Friday.

Obama acknowledged the damage, saying Thursday that it’s “legitimate” to expect he has to “win back some credibility” from the American public.

“My intention in terms of winning back the confidence of the American people is just to work as hard as I can. We’re just going to keep on chipping away at this until the job is done.”

He has two potential advantages: an economy that continues to grow, however slowly, and still-decent support from his party.

Democrats in the House of Representatives were surly with administration officials early in the week, and 39 of the House’s 200 Democrats voted for a Republican health care fix Friday. But they were careful not to tear into Obama.

Rep. Nick Rahall, D-W.Va., said the reaction to the law in his district was “very bad, rotten,” but he added, “I don’t see this as a blow to the president. I see it as a call to work together. The problems are solvable.”

Analysts agree that there’s time – and opportunity.

“If you go back historically, it’s not impossible for a president to turn the corner on these low ratings,” said Michael Dimock, the director of the Pew Research Center for the People and the Press.

He noted that Reagan hit a rocky stretch “but it didn’t end up framing his legacy.” Others, such as Jimmy Carter and Bush, are often saddled with images of a largely unhappy and dissatisfied public.

To date, Dimock said, Obama’s long-term popularity trajectory shows spikes and valleys rather than a continued decline. The president recovered from a previous low in the summer of 2011, during the first major debate over raising the debt ceiling.

“There’s not enough evidence to say this is the end for Obama, that these numbers can’t turn around, that he has fundamentally lost the public’s confidence,” Dimock said. “Both his own history and a broader history suggest that it is possible.”

Yet to do that, Dimock said, Obama will need a more robust economic recovery – and a health care program that works.

“Like George W. Bush, his presidency is inexorably linked to a specific policy,” Dimock said. “As long as the war in Iraq was declining in public popularity and support, so, too, was Bush’s presidency. Obama’s presidency is hooked to the signature policy of his first term.”

Coming up next: a new fight over federal debt and spending. Budget negotiators have until Dec. 13 to write a budget plan, and most spending authority runs through mid-January. Unless Congress and Obama agree to a fix, another government shutdown looms. It all means even more reasons for Americans to be skeptical of their government.

None of this will be easy for Obama to overcome, at least anytime soon.

“When you lose that trust,” Walden said, “it’s very difficult to get it back.”

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